Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,6,Mod(1,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("690.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(110.664835671\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 690.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.00000 | 0.707107 | ||||||||
\(3\) | −9.00000 | −0.577350 | ||||||||
\(4\) | 16.0000 | 0.500000 | ||||||||
\(5\) | −25.0000 | −0.447214 | ||||||||
\(6\) | −36.0000 | −0.408248 | ||||||||
\(7\) | 32.0000 | 0.246834 | 0.123417 | − | 0.992355i | \(-0.460615\pi\) | ||||
0.123417 | + | 0.992355i | \(0.460615\pi\) | |||||||
\(8\) | 64.0000 | 0.353553 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | −100.000 | −0.316228 | ||||||||
\(11\) | 372.000 | 0.926960 | 0.463480 | − | 0.886107i | \(-0.346600\pi\) | ||||
0.463480 | + | 0.886107i | \(0.346600\pi\) | |||||||
\(12\) | −144.000 | −0.288675 | ||||||||
\(13\) | −382.000 | −0.626910 | −0.313455 | − | 0.949603i | \(-0.601486\pi\) | ||||
−0.313455 | + | 0.949603i | \(0.601486\pi\) | |||||||
\(14\) | 128.000 | 0.174538 | ||||||||
\(15\) | 225.000 | 0.258199 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | −846.000 | −0.709983 | −0.354992 | − | 0.934869i | \(-0.615516\pi\) | ||||
−0.354992 | + | 0.934869i | \(0.615516\pi\) | |||||||
\(18\) | 324.000 | 0.235702 | ||||||||
\(19\) | 1232.00 | 0.782937 | 0.391468 | − | 0.920192i | \(-0.371967\pi\) | ||||
0.391468 | + | 0.920192i | \(0.371967\pi\) | |||||||
\(20\) | −400.000 | −0.223607 | ||||||||
\(21\) | −288.000 | −0.142510 | ||||||||
\(22\) | 1488.00 | 0.655460 | ||||||||
\(23\) | −529.000 | −0.208514 | ||||||||
\(24\) | −576.000 | −0.204124 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | −1528.00 | −0.443292 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | 512.000 | 0.123417 | ||||||||
\(29\) | −1302.00 | −0.287486 | −0.143743 | − | 0.989615i | \(-0.545914\pi\) | ||||
−0.143743 | + | 0.989615i | \(0.545914\pi\) | |||||||
\(30\) | 900.000 | 0.182574 | ||||||||
\(31\) | 5840.00 | 1.09146 | 0.545731 | − | 0.837960i | \(-0.316252\pi\) | ||||
0.545731 | + | 0.837960i | \(0.316252\pi\) | |||||||
\(32\) | 1024.00 | 0.176777 | ||||||||
\(33\) | −3348.00 | −0.535181 | ||||||||
\(34\) | −3384.00 | −0.502034 | ||||||||
\(35\) | −800.000 | −0.110387 | ||||||||
\(36\) | 1296.00 | 0.166667 | ||||||||
\(37\) | −3862.00 | −0.463776 | −0.231888 | − | 0.972743i | \(-0.574490\pi\) | ||||
−0.231888 | + | 0.972743i | \(0.574490\pi\) | |||||||
\(38\) | 4928.00 | 0.553620 | ||||||||
\(39\) | 3438.00 | 0.361946 | ||||||||
\(40\) | −1600.00 | −0.158114 | ||||||||
\(41\) | −15774.0 | −1.46549 | −0.732744 | − | 0.680505i | \(-0.761761\pi\) | ||||
−0.732744 | + | 0.680505i | \(0.761761\pi\) | |||||||
\(42\) | −1152.00 | −0.100770 | ||||||||
\(43\) | 12524.0 | 1.03293 | 0.516466 | − | 0.856308i | \(-0.327247\pi\) | ||||
0.516466 | + | 0.856308i | \(0.327247\pi\) | |||||||
\(44\) | 5952.00 | 0.463480 | ||||||||
\(45\) | −2025.00 | −0.149071 | ||||||||
\(46\) | −2116.00 | −0.147442 | ||||||||
\(47\) | 21888.0 | 1.44531 | 0.722656 | − | 0.691208i | \(-0.242921\pi\) | ||||
0.722656 | + | 0.691208i | \(0.242921\pi\) | |||||||
\(48\) | −2304.00 | −0.144338 | ||||||||
\(49\) | −15783.0 | −0.939073 | ||||||||
\(50\) | 2500.00 | 0.141421 | ||||||||
\(51\) | 7614.00 | 0.409909 | ||||||||
\(52\) | −6112.00 | −0.313455 | ||||||||
\(53\) | −1734.00 | −0.0847929 | −0.0423964 | − | 0.999101i | \(-0.513499\pi\) | ||||
−0.0423964 | + | 0.999101i | \(0.513499\pi\) | |||||||
\(54\) | −2916.00 | −0.136083 | ||||||||
\(55\) | −9300.00 | −0.414549 | ||||||||
\(56\) | 2048.00 | 0.0872690 | ||||||||
\(57\) | −11088.0 | −0.452029 | ||||||||
\(58\) | −5208.00 | −0.203283 | ||||||||
\(59\) | 1908.00 | 0.0713589 | 0.0356795 | − | 0.999363i | \(-0.488640\pi\) | ||||
0.0356795 | + | 0.999363i | \(0.488640\pi\) | |||||||
\(60\) | 3600.00 | 0.129099 | ||||||||
\(61\) | −34678.0 | −1.19324 | −0.596622 | − | 0.802522i | \(-0.703491\pi\) | ||||
−0.596622 | + | 0.802522i | \(0.703491\pi\) | |||||||
\(62\) | 23360.0 | 0.771780 | ||||||||
\(63\) | 2592.00 | 0.0822780 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | 9550.00 | 0.280363 | ||||||||
\(66\) | −13392.0 | −0.378430 | ||||||||
\(67\) | 22892.0 | 0.623012 | 0.311506 | − | 0.950244i | \(-0.399167\pi\) | ||||
0.311506 | + | 0.950244i | \(0.399167\pi\) | |||||||
\(68\) | −13536.0 | −0.354992 | ||||||||
\(69\) | 4761.00 | 0.120386 | ||||||||
\(70\) | −3200.00 | −0.0780557 | ||||||||
\(71\) | 22596.0 | 0.531968 | 0.265984 | − | 0.963977i | \(-0.414303\pi\) | ||||
0.265984 | + | 0.963977i | \(0.414303\pi\) | |||||||
\(72\) | 5184.00 | 0.117851 | ||||||||
\(73\) | 57602.0 | 1.26512 | 0.632558 | − | 0.774513i | \(-0.282005\pi\) | ||||
0.632558 | + | 0.774513i | \(0.282005\pi\) | |||||||
\(74\) | −15448.0 | −0.327939 | ||||||||
\(75\) | −5625.00 | −0.115470 | ||||||||
\(76\) | 19712.0 | 0.391468 | ||||||||
\(77\) | 11904.0 | 0.228805 | ||||||||
\(78\) | 13752.0 | 0.255935 | ||||||||
\(79\) | −66352.0 | −1.19615 | −0.598076 | − | 0.801439i | \(-0.704068\pi\) | ||||
−0.598076 | + | 0.801439i | \(0.704068\pi\) | |||||||
\(80\) | −6400.00 | −0.111803 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | −63096.0 | −1.03626 | ||||||||
\(83\) | 33744.0 | 0.537652 | 0.268826 | − | 0.963189i | \(-0.413364\pi\) | ||||
0.268826 | + | 0.963189i | \(0.413364\pi\) | |||||||
\(84\) | −4608.00 | −0.0712548 | ||||||||
\(85\) | 21150.0 | 0.317514 | ||||||||
\(86\) | 50096.0 | 0.730394 | ||||||||
\(87\) | 11718.0 | 0.165980 | ||||||||
\(88\) | 23808.0 | 0.327730 | ||||||||
\(89\) | 36654.0 | 0.490508 | 0.245254 | − | 0.969459i | \(-0.421129\pi\) | ||||
0.245254 | + | 0.969459i | \(0.421129\pi\) | |||||||
\(90\) | −8100.00 | −0.105409 | ||||||||
\(91\) | −12224.0 | −0.154743 | ||||||||
\(92\) | −8464.00 | −0.104257 | ||||||||
\(93\) | −52560.0 | −0.630156 | ||||||||
\(94\) | 87552.0 | 1.02199 | ||||||||
\(95\) | −30800.0 | −0.350140 | ||||||||
\(96\) | −9216.00 | −0.102062 | ||||||||
\(97\) | 125174. | 1.35078 | 0.675390 | − | 0.737460i | \(-0.263975\pi\) | ||||
0.675390 | + | 0.737460i | \(0.263975\pi\) | |||||||
\(98\) | −63132.0 | −0.664025 | ||||||||
\(99\) | 30132.0 | 0.308987 | ||||||||
\(100\) | 10000.0 | 0.100000 | ||||||||
\(101\) | 86394.0 | 0.842714 | 0.421357 | − | 0.906895i | \(-0.361554\pi\) | ||||
0.421357 | + | 0.906895i | \(0.361554\pi\) | |||||||
\(102\) | 30456.0 | 0.289849 | ||||||||
\(103\) | 142952. | 1.32769 | 0.663846 | − | 0.747870i | \(-0.268923\pi\) | ||||
0.663846 | + | 0.747870i | \(0.268923\pi\) | |||||||
\(104\) | −24448.0 | −0.221646 | ||||||||
\(105\) | 7200.00 | 0.0637322 | ||||||||
\(106\) | −6936.00 | −0.0599576 | ||||||||
\(107\) | 153792. | 1.29860 | 0.649298 | − | 0.760534i | \(-0.275063\pi\) | ||||
0.649298 | + | 0.760534i | \(0.275063\pi\) | |||||||
\(108\) | −11664.0 | −0.0962250 | ||||||||
\(109\) | 27290.0 | 0.220007 | 0.110004 | − | 0.993931i | \(-0.464914\pi\) | ||||
0.110004 | + | 0.993931i | \(0.464914\pi\) | |||||||
\(110\) | −37200.0 | −0.293131 | ||||||||
\(111\) | 34758.0 | 0.267761 | ||||||||
\(112\) | 8192.00 | 0.0617085 | ||||||||
\(113\) | 140034. | 1.03166 | 0.515831 | − | 0.856690i | \(-0.327483\pi\) | ||||
0.515831 | + | 0.856690i | \(0.327483\pi\) | |||||||
\(114\) | −44352.0 | −0.319633 | ||||||||
\(115\) | 13225.0 | 0.0932505 | ||||||||
\(116\) | −20832.0 | −0.143743 | ||||||||
\(117\) | −30942.0 | −0.208970 | ||||||||
\(118\) | 7632.00 | 0.0504584 | ||||||||
\(119\) | −27072.0 | −0.175248 | ||||||||
\(120\) | 14400.0 | 0.0912871 | ||||||||
\(121\) | −22667.0 | −0.140744 | ||||||||
\(122\) | −138712. | −0.843751 | ||||||||
\(123\) | 141966. | 0.846100 | ||||||||
\(124\) | 93440.0 | 0.545731 | ||||||||
\(125\) | −15625.0 | −0.0894427 | ||||||||
\(126\) | 10368.0 | 0.0581793 | ||||||||
\(127\) | 109244. | 0.601019 | 0.300510 | − | 0.953779i | \(-0.402843\pi\) | ||||
0.300510 | + | 0.953779i | \(0.402843\pi\) | |||||||
\(128\) | 16384.0 | 0.0883883 | ||||||||
\(129\) | −112716. | −0.596364 | ||||||||
\(130\) | 38200.0 | 0.198246 | ||||||||
\(131\) | −53100.0 | −0.270344 | −0.135172 | − | 0.990822i | \(-0.543159\pi\) | ||||
−0.135172 | + | 0.990822i | \(0.543159\pi\) | |||||||
\(132\) | −53568.0 | −0.267590 | ||||||||
\(133\) | 39424.0 | 0.193255 | ||||||||
\(134\) | 91568.0 | 0.440536 | ||||||||
\(135\) | 18225.0 | 0.0860663 | ||||||||
\(136\) | −54144.0 | −0.251017 | ||||||||
\(137\) | −282942. | −1.28794 | −0.643971 | − | 0.765050i | \(-0.722714\pi\) | ||||
−0.643971 | + | 0.765050i | \(0.722714\pi\) | |||||||
\(138\) | 19044.0 | 0.0851257 | ||||||||
\(139\) | 367628. | 1.61388 | 0.806941 | − | 0.590633i | \(-0.201122\pi\) | ||||
0.806941 | + | 0.590633i | \(0.201122\pi\) | |||||||
\(140\) | −12800.0 | −0.0551937 | ||||||||
\(141\) | −196992. | −0.834451 | ||||||||
\(142\) | 90384.0 | 0.376158 | ||||||||
\(143\) | −142104. | −0.581121 | ||||||||
\(144\) | 20736.0 | 0.0833333 | ||||||||
\(145\) | 32550.0 | 0.128567 | ||||||||
\(146\) | 230408. | 0.894572 | ||||||||
\(147\) | 142047. | 0.542174 | ||||||||
\(148\) | −61792.0 | −0.231888 | ||||||||
\(149\) | 11034.0 | 0.0407162 | 0.0203581 | − | 0.999793i | \(-0.493519\pi\) | ||||
0.0203581 | + | 0.999793i | \(0.493519\pi\) | |||||||
\(150\) | −22500.0 | −0.0816497 | ||||||||
\(151\) | 452768. | 1.61597 | 0.807985 | − | 0.589203i | \(-0.200558\pi\) | ||||
0.807985 | + | 0.589203i | \(0.200558\pi\) | |||||||
\(152\) | 78848.0 | 0.276810 | ||||||||
\(153\) | −68526.0 | −0.236661 | ||||||||
\(154\) | 47616.0 | 0.161790 | ||||||||
\(155\) | −146000. | −0.488117 | ||||||||
\(156\) | 55008.0 | 0.180973 | ||||||||
\(157\) | 371474. | 1.20276 | 0.601380 | − | 0.798963i | \(-0.294618\pi\) | ||||
0.601380 | + | 0.798963i | \(0.294618\pi\) | |||||||
\(158\) | −265408. | −0.845807 | ||||||||
\(159\) | 15606.0 | 0.0489552 | ||||||||
\(160\) | −25600.0 | −0.0790569 | ||||||||
\(161\) | −16928.0 | −0.0514684 | ||||||||
\(162\) | 26244.0 | 0.0785674 | ||||||||
\(163\) | −357676. | −1.05444 | −0.527219 | − | 0.849730i | \(-0.676765\pi\) | ||||
−0.527219 | + | 0.849730i | \(0.676765\pi\) | |||||||
\(164\) | −252384. | −0.732744 | ||||||||
\(165\) | 83700.0 | 0.239340 | ||||||||
\(166\) | 134976. | 0.380177 | ||||||||
\(167\) | 533808. | 1.48113 | 0.740566 | − | 0.671983i | \(-0.234557\pi\) | ||||
0.740566 | + | 0.671983i | \(0.234557\pi\) | |||||||
\(168\) | −18432.0 | −0.0503848 | ||||||||
\(169\) | −225369. | −0.606984 | ||||||||
\(170\) | 84600.0 | 0.224516 | ||||||||
\(171\) | 99792.0 | 0.260979 | ||||||||
\(172\) | 200384. | 0.516466 | ||||||||
\(173\) | 523590. | 1.33007 | 0.665037 | − | 0.746810i | \(-0.268416\pi\) | ||||
0.665037 | + | 0.746810i | \(0.268416\pi\) | |||||||
\(174\) | 46872.0 | 0.117365 | ||||||||
\(175\) | 20000.0 | 0.0493668 | ||||||||
\(176\) | 95232.0 | 0.231740 | ||||||||
\(177\) | −17172.0 | −0.0411991 | ||||||||
\(178\) | 146616. | 0.346842 | ||||||||
\(179\) | −447180. | −1.04316 | −0.521579 | − | 0.853203i | \(-0.674657\pi\) | ||||
−0.521579 | + | 0.853203i | \(0.674657\pi\) | |||||||
\(180\) | −32400.0 | −0.0745356 | ||||||||
\(181\) | 160754. | 0.364725 | 0.182362 | − | 0.983231i | \(-0.441626\pi\) | ||||
0.182362 | + | 0.983231i | \(0.441626\pi\) | |||||||
\(182\) | −48896.0 | −0.109420 | ||||||||
\(183\) | 312102. | 0.688920 | ||||||||
\(184\) | −33856.0 | −0.0737210 | ||||||||
\(185\) | 96550.0 | 0.207407 | ||||||||
\(186\) | −210240. | −0.445587 | ||||||||
\(187\) | −314712. | −0.658126 | ||||||||
\(188\) | 350208. | 0.722656 | ||||||||
\(189\) | −23328.0 | −0.0475032 | ||||||||
\(190\) | −123200. | −0.247586 | ||||||||
\(191\) | 659400. | 1.30787 | 0.653936 | − | 0.756550i | \(-0.273116\pi\) | ||||
0.653936 | + | 0.756550i | \(0.273116\pi\) | |||||||
\(192\) | −36864.0 | −0.0721688 | ||||||||
\(193\) | −656494. | −1.26864 | −0.634319 | − | 0.773072i | \(-0.718719\pi\) | ||||
−0.634319 | + | 0.773072i | \(0.718719\pi\) | |||||||
\(194\) | 500696. | 0.955146 | ||||||||
\(195\) | −85950.0 | −0.161867 | ||||||||
\(196\) | −252528. | −0.469537 | ||||||||
\(197\) | −852738. | −1.56549 | −0.782745 | − | 0.622343i | \(-0.786181\pi\) | ||||
−0.782745 | + | 0.622343i | \(0.786181\pi\) | |||||||
\(198\) | 120528. | 0.218487 | ||||||||
\(199\) | 412496. | 0.738392 | 0.369196 | − | 0.929352i | \(-0.379633\pi\) | ||||
0.369196 | + | 0.929352i | \(0.379633\pi\) | |||||||
\(200\) | 40000.0 | 0.0707107 | ||||||||
\(201\) | −206028. | −0.359696 | ||||||||
\(202\) | 345576. | 0.595889 | ||||||||
\(203\) | −41664.0 | −0.0709612 | ||||||||
\(204\) | 121824. | 0.204954 | ||||||||
\(205\) | 394350. | 0.655386 | ||||||||
\(206\) | 571808. | 0.938820 | ||||||||
\(207\) | −42849.0 | −0.0695048 | ||||||||
\(208\) | −97792.0 | −0.156727 | ||||||||
\(209\) | 458304. | 0.725751 | ||||||||
\(210\) | 28800.0 | 0.0450655 | ||||||||
\(211\) | 1.01373e6 | 1.56753 | 0.783767 | − | 0.621055i | \(-0.213296\pi\) | ||||
0.783767 | + | 0.621055i | \(0.213296\pi\) | |||||||
\(212\) | −27744.0 | −0.0423964 | ||||||||
\(213\) | −203364. | −0.307132 | ||||||||
\(214\) | 615168. | 0.918247 | ||||||||
\(215\) | −313100. | −0.461941 | ||||||||
\(216\) | −46656.0 | −0.0680414 | ||||||||
\(217\) | 186880. | 0.269410 | ||||||||
\(218\) | 109160. | 0.155569 | ||||||||
\(219\) | −518418. | −0.730415 | ||||||||
\(220\) | −148800. | −0.207275 | ||||||||
\(221\) | 323172. | 0.445095 | ||||||||
\(222\) | 139032. | 0.189336 | ||||||||
\(223\) | −182164. | −0.245302 | −0.122651 | − | 0.992450i | \(-0.539140\pi\) | ||||
−0.122651 | + | 0.992450i | \(0.539140\pi\) | |||||||
\(224\) | 32768.0 | 0.0436345 | ||||||||
\(225\) | 50625.0 | 0.0666667 | ||||||||
\(226\) | 560136. | 0.729495 | ||||||||
\(227\) | −70848.0 | −0.0912563 | −0.0456282 | − | 0.998958i | \(-0.514529\pi\) | ||||
−0.0456282 | + | 0.998958i | \(0.514529\pi\) | |||||||
\(228\) | −177408. | −0.226014 | ||||||||
\(229\) | −116254. | −0.146494 | −0.0732469 | − | 0.997314i | \(-0.523336\pi\) | ||||
−0.0732469 | + | 0.997314i | \(0.523336\pi\) | |||||||
\(230\) | 52900.0 | 0.0659380 | ||||||||
\(231\) | −107136. | −0.132101 | ||||||||
\(232\) | −83328.0 | −0.101641 | ||||||||
\(233\) | 1.30915e6 | 1.57979 | 0.789893 | − | 0.613245i | \(-0.210136\pi\) | ||||
0.789893 | + | 0.613245i | \(0.210136\pi\) | |||||||
\(234\) | −123768. | −0.147764 | ||||||||
\(235\) | −547200. | −0.646363 | ||||||||
\(236\) | 30528.0 | 0.0356795 | ||||||||
\(237\) | 597168. | 0.690599 | ||||||||
\(238\) | −108288. | −0.123919 | ||||||||
\(239\) | −836220. | −0.946947 | −0.473474 | − | 0.880808i | \(-0.657000\pi\) | ||||
−0.473474 | + | 0.880808i | \(0.657000\pi\) | |||||||
\(240\) | 57600.0 | 0.0645497 | ||||||||
\(241\) | 640490. | 0.710346 | 0.355173 | − | 0.934801i | \(-0.384422\pi\) | ||||
0.355173 | + | 0.934801i | \(0.384422\pi\) | |||||||
\(242\) | −90668.0 | −0.0995212 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | −554848. | −0.596622 | ||||||||
\(245\) | 394575. | 0.419966 | ||||||||
\(246\) | 567864. | 0.598283 | ||||||||
\(247\) | −470624. | −0.490831 | ||||||||
\(248\) | 373760. | 0.385890 | ||||||||
\(249\) | −303696. | −0.310414 | ||||||||
\(250\) | −62500.0 | −0.0632456 | ||||||||
\(251\) | 1.45040e6 | 1.45313 | 0.726565 | − | 0.687097i | \(-0.241115\pi\) | ||||
0.726565 | + | 0.687097i | \(0.241115\pi\) | |||||||
\(252\) | 41472.0 | 0.0411390 | ||||||||
\(253\) | −196788. | −0.193285 | ||||||||
\(254\) | 436976. | 0.424985 | ||||||||
\(255\) | −190350. | −0.183317 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | 721218. | 0.681136 | 0.340568 | − | 0.940220i | \(-0.389381\pi\) | ||||
0.340568 | + | 0.940220i | \(0.389381\pi\) | |||||||
\(258\) | −450864. | −0.421693 | ||||||||
\(259\) | −123584. | −0.114476 | ||||||||
\(260\) | 152800. | 0.140181 | ||||||||
\(261\) | −105462. | −0.0958285 | ||||||||
\(262\) | −212400. | −0.191162 | ||||||||
\(263\) | 762288. | 0.679563 | 0.339781 | − | 0.940504i | \(-0.389647\pi\) | ||||
0.339781 | + | 0.940504i | \(0.389647\pi\) | |||||||
\(264\) | −214272. | −0.189215 | ||||||||
\(265\) | 43350.0 | 0.0379205 | ||||||||
\(266\) | 157696. | 0.136652 | ||||||||
\(267\) | −329886. | −0.283195 | ||||||||
\(268\) | 366272. | 0.311506 | ||||||||
\(269\) | −1.61187e6 | −1.35815 | −0.679077 | − | 0.734067i | \(-0.737620\pi\) | ||||
−0.679077 | + | 0.734067i | \(0.737620\pi\) | |||||||
\(270\) | 72900.0 | 0.0608581 | ||||||||
\(271\) | −817048. | −0.675810 | −0.337905 | − | 0.941180i | \(-0.609718\pi\) | ||||
−0.337905 | + | 0.941180i | \(0.609718\pi\) | |||||||
\(272\) | −216576. | −0.177496 | ||||||||
\(273\) | 110016. | 0.0893407 | ||||||||
\(274\) | −1.13177e6 | −0.910712 | ||||||||
\(275\) | 232500. | 0.185392 | ||||||||
\(276\) | 76176.0 | 0.0601929 | ||||||||
\(277\) | 1.58794e6 | 1.24347 | 0.621733 | − | 0.783229i | \(-0.286429\pi\) | ||||
0.621733 | + | 0.783229i | \(0.286429\pi\) | |||||||
\(278\) | 1.47051e6 | 1.14119 | ||||||||
\(279\) | 473040. | 0.363821 | ||||||||
\(280\) | −51200.0 | −0.0390279 | ||||||||
\(281\) | −1.03365e6 | −0.780922 | −0.390461 | − | 0.920619i | \(-0.627684\pi\) | ||||
−0.390461 | + | 0.920619i | \(0.627684\pi\) | |||||||
\(282\) | −787968. | −0.590046 | ||||||||
\(283\) | −560620. | −0.416105 | −0.208052 | − | 0.978118i | \(-0.566712\pi\) | ||||
−0.208052 | + | 0.978118i | \(0.566712\pi\) | |||||||
\(284\) | 361536. | 0.265984 | ||||||||
\(285\) | 277200. | 0.202153 | ||||||||
\(286\) | −568416. | −0.410914 | ||||||||
\(287\) | −504768. | −0.361732 | ||||||||
\(288\) | 82944.0 | 0.0589256 | ||||||||
\(289\) | −704141. | −0.495924 | ||||||||
\(290\) | 130200. | 0.0909109 | ||||||||
\(291\) | −1.12657e6 | −0.779874 | ||||||||
\(292\) | 921632. | 0.632558 | ||||||||
\(293\) | −2.41287e6 | −1.64197 | −0.820984 | − | 0.570951i | \(-0.806575\pi\) | ||||
−0.820984 | + | 0.570951i | \(0.806575\pi\) | |||||||
\(294\) | 568188. | 0.383375 | ||||||||
\(295\) | −47700.0 | −0.0319127 | ||||||||
\(296\) | −247168. | −0.163969 | ||||||||
\(297\) | −271188. | −0.178394 | ||||||||
\(298\) | 44136.0 | 0.0287907 | ||||||||
\(299\) | 202078. | 0.130720 | ||||||||
\(300\) | −90000.0 | −0.0577350 | ||||||||
\(301\) | 400768. | 0.254963 | ||||||||
\(302\) | 1.81107e6 | 1.14266 | ||||||||
\(303\) | −777546. | −0.486541 | ||||||||
\(304\) | 315392. | 0.195734 | ||||||||
\(305\) | 866950. | 0.533635 | ||||||||
\(306\) | −274104. | −0.167345 | ||||||||
\(307\) | 2.25729e6 | 1.36692 | 0.683458 | − | 0.729990i | \(-0.260475\pi\) | ||||
0.683458 | + | 0.729990i | \(0.260475\pi\) | |||||||
\(308\) | 190464. | 0.114403 | ||||||||
\(309\) | −1.28657e6 | −0.766543 | ||||||||
\(310\) | −584000. | −0.345151 | ||||||||
\(311\) | −2.02948e6 | −1.18982 | −0.594912 | − | 0.803791i | \(-0.702813\pi\) | ||||
−0.594912 | + | 0.803791i | \(0.702813\pi\) | |||||||
\(312\) | 220032. | 0.127967 | ||||||||
\(313\) | 2.48625e6 | 1.43444 | 0.717221 | − | 0.696845i | \(-0.245414\pi\) | ||||
0.717221 | + | 0.696845i | \(0.245414\pi\) | |||||||
\(314\) | 1.48590e6 | 0.850480 | ||||||||
\(315\) | −64800.0 | −0.0367958 | ||||||||
\(316\) | −1.06163e6 | −0.598076 | ||||||||
\(317\) | 2.10065e6 | 1.17410 | 0.587052 | − | 0.809549i | \(-0.300289\pi\) | ||||
0.587052 | + | 0.809549i | \(0.300289\pi\) | |||||||
\(318\) | 62424.0 | 0.0346166 | ||||||||
\(319\) | −484344. | −0.266488 | ||||||||
\(320\) | −102400. | −0.0559017 | ||||||||
\(321\) | −1.38413e6 | −0.749745 | ||||||||
\(322\) | −67712.0 | −0.0363937 | ||||||||
\(323\) | −1.04227e6 | −0.555872 | ||||||||
\(324\) | 104976. | 0.0555556 | ||||||||
\(325\) | −238750. | −0.125382 | ||||||||
\(326\) | −1.43070e6 | −0.745600 | ||||||||
\(327\) | −245610. | −0.127021 | ||||||||
\(328\) | −1.00954e6 | −0.518128 | ||||||||
\(329\) | 700416. | 0.356752 | ||||||||
\(330\) | 334800. | 0.169239 | ||||||||
\(331\) | −2.35508e6 | −1.18150 | −0.590752 | − | 0.806853i | \(-0.701169\pi\) | ||||
−0.590752 | + | 0.806853i | \(0.701169\pi\) | |||||||
\(332\) | 539904. | 0.268826 | ||||||||
\(333\) | −312822. | −0.154592 | ||||||||
\(334\) | 2.13523e6 | 1.04732 | ||||||||
\(335\) | −572300. | −0.278620 | ||||||||
\(336\) | −73728.0 | −0.0356274 | ||||||||
\(337\) | −2.32191e6 | −1.11371 | −0.556854 | − | 0.830610i | \(-0.687992\pi\) | ||||
−0.556854 | + | 0.830610i | \(0.687992\pi\) | |||||||
\(338\) | −901476. | −0.429203 | ||||||||
\(339\) | −1.26031e6 | −0.595630 | ||||||||
\(340\) | 338400. | 0.158757 | ||||||||
\(341\) | 2.17248e6 | 1.01174 | ||||||||
\(342\) | 399168. | 0.184540 | ||||||||
\(343\) | −1.04288e6 | −0.478629 | ||||||||
\(344\) | 801536. | 0.365197 | ||||||||
\(345\) | −119025. | −0.0538382 | ||||||||
\(346\) | 2.09436e6 | 0.940505 | ||||||||
\(347\) | 650940. | 0.290213 | 0.145107 | − | 0.989416i | \(-0.453647\pi\) | ||||
0.145107 | + | 0.989416i | \(0.453647\pi\) | |||||||
\(348\) | 187488. | 0.0829899 | ||||||||
\(349\) | 373310. | 0.164061 | 0.0820306 | − | 0.996630i | \(-0.473859\pi\) | ||||
0.0820306 | + | 0.996630i | \(0.473859\pi\) | |||||||
\(350\) | 80000.0 | 0.0349076 | ||||||||
\(351\) | 278478. | 0.120649 | ||||||||
\(352\) | 380928. | 0.163865 | ||||||||
\(353\) | −2.92097e6 | −1.24764 | −0.623822 | − | 0.781566i | \(-0.714421\pi\) | ||||
−0.623822 | + | 0.781566i | \(0.714421\pi\) | |||||||
\(354\) | −68688.0 | −0.0291322 | ||||||||
\(355\) | −564900. | −0.237903 | ||||||||
\(356\) | 586464. | 0.245254 | ||||||||
\(357\) | 243648. | 0.101179 | ||||||||
\(358\) | −1.78872e6 | −0.737624 | ||||||||
\(359\) | −3.58286e6 | −1.46722 | −0.733608 | − | 0.679573i | \(-0.762165\pi\) | ||||
−0.733608 | + | 0.679573i | \(0.762165\pi\) | |||||||
\(360\) | −129600. | −0.0527046 | ||||||||
\(361\) | −958275. | −0.387010 | ||||||||
\(362\) | 643016. | 0.257899 | ||||||||
\(363\) | 204003. | 0.0812587 | ||||||||
\(364\) | −195584. | −0.0773713 | ||||||||
\(365\) | −1.44005e6 | −0.565777 | ||||||||
\(366\) | 1.24841e6 | 0.487140 | ||||||||
\(367\) | 2.85913e6 | 1.10807 | 0.554037 | − | 0.832492i | \(-0.313087\pi\) | ||||
0.554037 | + | 0.832492i | \(0.313087\pi\) | |||||||
\(368\) | −135424. | −0.0521286 | ||||||||
\(369\) | −1.27769e6 | −0.488496 | ||||||||
\(370\) | 386200. | 0.146659 | ||||||||
\(371\) | −55488.0 | −0.0209298 | ||||||||
\(372\) | −840960. | −0.315078 | ||||||||
\(373\) | −1.57197e6 | −0.585023 | −0.292512 | − | 0.956262i | \(-0.594491\pi\) | ||||
−0.292512 | + | 0.956262i | \(0.594491\pi\) | |||||||
\(374\) | −1.25885e6 | −0.465366 | ||||||||
\(375\) | 140625. | 0.0516398 | ||||||||
\(376\) | 1.40083e6 | 0.510995 | ||||||||
\(377\) | 497364. | 0.180227 | ||||||||
\(378\) | −93312.0 | −0.0335898 | ||||||||
\(379\) | 492032. | 0.175952 | 0.0879762 | − | 0.996123i | \(-0.471960\pi\) | ||||
0.0879762 | + | 0.996123i | \(0.471960\pi\) | |||||||
\(380\) | −492800. | −0.175070 | ||||||||
\(381\) | −983196. | −0.346999 | ||||||||
\(382\) | 2.63760e6 | 0.924806 | ||||||||
\(383\) | −1.82758e6 | −0.636617 | −0.318309 | − | 0.947987i | \(-0.603115\pi\) | ||||
−0.318309 | + | 0.947987i | \(0.603115\pi\) | |||||||
\(384\) | −147456. | −0.0510310 | ||||||||
\(385\) | −297600. | −0.102325 | ||||||||
\(386\) | −2.62598e6 | −0.897062 | ||||||||
\(387\) | 1.01444e6 | 0.344311 | ||||||||
\(388\) | 2.00278e6 | 0.675390 | ||||||||
\(389\) | −3.94810e6 | −1.32286 | −0.661431 | − | 0.750006i | \(-0.730050\pi\) | ||||
−0.661431 | + | 0.750006i | \(0.730050\pi\) | |||||||
\(390\) | −343800. | −0.114458 | ||||||||
\(391\) | 447534. | 0.148042 | ||||||||
\(392\) | −1.01011e6 | −0.332012 | ||||||||
\(393\) | 477900. | 0.156083 | ||||||||
\(394\) | −3.41095e6 | −1.10697 | ||||||||
\(395\) | 1.65880e6 | 0.534935 | ||||||||
\(396\) | 482112. | 0.154493 | ||||||||
\(397\) | −745630. | −0.237436 | −0.118718 | − | 0.992928i | \(-0.537878\pi\) | ||||
−0.118718 | + | 0.992928i | \(0.537878\pi\) | |||||||
\(398\) | 1.64998e6 | 0.522122 | ||||||||
\(399\) | −354816. | −0.111576 | ||||||||
\(400\) | 160000. | 0.0500000 | ||||||||
\(401\) | 5.08738e6 | 1.57991 | 0.789957 | − | 0.613162i | \(-0.210103\pi\) | ||||
0.789957 | + | 0.613162i | \(0.210103\pi\) | |||||||
\(402\) | −824112. | −0.254344 | ||||||||
\(403\) | −2.23088e6 | −0.684248 | ||||||||
\(404\) | 1.38230e6 | 0.421357 | ||||||||
\(405\) | −164025. | −0.0496904 | ||||||||
\(406\) | −166656. | −0.0501771 | ||||||||
\(407\) | −1.43666e6 | −0.429902 | ||||||||
\(408\) | 487296. | 0.144925 | ||||||||
\(409\) | 2.12844e6 | 0.629149 | 0.314575 | − | 0.949233i | \(-0.398138\pi\) | ||||
0.314575 | + | 0.949233i | \(0.398138\pi\) | |||||||
\(410\) | 1.57740e6 | 0.463428 | ||||||||
\(411\) | 2.54648e6 | 0.743593 | ||||||||
\(412\) | 2.28723e6 | 0.663846 | ||||||||
\(413\) | 61056.0 | 0.0176138 | ||||||||
\(414\) | −171396. | −0.0491473 | ||||||||
\(415\) | −843600. | −0.240445 | ||||||||
\(416\) | −391168. | −0.110823 | ||||||||
\(417\) | −3.30865e6 | −0.931775 | ||||||||
\(418\) | 1.83322e6 | 0.513184 | ||||||||
\(419\) | 5.44016e6 | 1.51383 | 0.756915 | − | 0.653514i | \(-0.226706\pi\) | ||||
0.756915 | + | 0.653514i | \(0.226706\pi\) | |||||||
\(420\) | 115200. | 0.0318661 | ||||||||
\(421\) | −1.23103e6 | −0.338504 | −0.169252 | − | 0.985573i | \(-0.554135\pi\) | ||||
−0.169252 | + | 0.985573i | \(0.554135\pi\) | |||||||
\(422\) | 4.05493e6 | 1.10841 | ||||||||
\(423\) | 1.77293e6 | 0.481770 | ||||||||
\(424\) | −110976. | −0.0299788 | ||||||||
\(425\) | −528750. | −0.141997 | ||||||||
\(426\) | −813456. | −0.217175 | ||||||||
\(427\) | −1.10970e6 | −0.294533 | ||||||||
\(428\) | 2.46067e6 | 0.649298 | ||||||||
\(429\) | 1.27894e6 | 0.335510 | ||||||||
\(430\) | −1.25240e6 | −0.326642 | ||||||||
\(431\) | 298056. | 0.0772867 | 0.0386433 | − | 0.999253i | \(-0.487696\pi\) | ||||
0.0386433 | + | 0.999253i | \(0.487696\pi\) | |||||||
\(432\) | −186624. | −0.0481125 | ||||||||
\(433\) | 569126. | 0.145878 | 0.0729388 | − | 0.997336i | \(-0.476762\pi\) | ||||
0.0729388 | + | 0.997336i | \(0.476762\pi\) | |||||||
\(434\) | 747520. | 0.190502 | ||||||||
\(435\) | −292950. | −0.0742284 | ||||||||
\(436\) | 436640. | 0.110004 | ||||||||
\(437\) | −651728. | −0.163254 | ||||||||
\(438\) | −2.07367e6 | −0.516482 | ||||||||
\(439\) | −4.10634e6 | −1.01694 | −0.508468 | − | 0.861081i | \(-0.669788\pi\) | ||||
−0.508468 | + | 0.861081i | \(0.669788\pi\) | |||||||
\(440\) | −595200. | −0.146565 | ||||||||
\(441\) | −1.27842e6 | −0.313024 | ||||||||
\(442\) | 1.29269e6 | 0.314730 | ||||||||
\(443\) | −3.03196e6 | −0.734030 | −0.367015 | − | 0.930215i | \(-0.619620\pi\) | ||||
−0.367015 | + | 0.930215i | \(0.619620\pi\) | |||||||
\(444\) | 556128. | 0.133881 | ||||||||
\(445\) | −916350. | −0.219362 | ||||||||
\(446\) | −728656. | −0.173454 | ||||||||
\(447\) | −99306.0 | −0.0235075 | ||||||||
\(448\) | 131072. | 0.0308542 | ||||||||
\(449\) | 1.46039e6 | 0.341865 | 0.170932 | − | 0.985283i | \(-0.445322\pi\) | ||||
0.170932 | + | 0.985283i | \(0.445322\pi\) | |||||||
\(450\) | 202500. | 0.0471405 | ||||||||
\(451\) | −5.86793e6 | −1.35845 | ||||||||
\(452\) | 2.24054e6 | 0.515831 | ||||||||
\(453\) | −4.07491e6 | −0.932981 | ||||||||
\(454\) | −283392. | −0.0645280 | ||||||||
\(455\) | 305600. | 0.0692030 | ||||||||
\(456\) | −709632. | −0.159816 | ||||||||
\(457\) | 7.47088e6 | 1.67333 | 0.836664 | − | 0.547716i | \(-0.184503\pi\) | ||||
0.836664 | + | 0.547716i | \(0.184503\pi\) | |||||||
\(458\) | −465016. | −0.103587 | ||||||||
\(459\) | 616734. | 0.136636 | ||||||||
\(460\) | 211600. | 0.0466252 | ||||||||
\(461\) | −1.33997e6 | −0.293660 | −0.146830 | − | 0.989162i | \(-0.546907\pi\) | ||||
−0.146830 | + | 0.989162i | \(0.546907\pi\) | |||||||
\(462\) | −428544. | −0.0934094 | ||||||||
\(463\) | 3.31408e6 | 0.718474 | 0.359237 | − | 0.933246i | \(-0.383037\pi\) | ||||
0.359237 | + | 0.933246i | \(0.383037\pi\) | |||||||
\(464\) | −333312. | −0.0718714 | ||||||||
\(465\) | 1.31400e6 | 0.281814 | ||||||||
\(466\) | 5.23658e6 | 1.11708 | ||||||||
\(467\) | 2.41502e6 | 0.512424 | 0.256212 | − | 0.966621i | \(-0.417526\pi\) | ||||
0.256212 | + | 0.966621i | \(0.417526\pi\) | |||||||
\(468\) | −495072. | −0.104485 | ||||||||
\(469\) | 732544. | 0.153781 | ||||||||
\(470\) | −2.18880e6 | −0.457048 | ||||||||
\(471\) | −3.34327e6 | −0.694414 | ||||||||
\(472\) | 122112. | 0.0252292 | ||||||||
\(473\) | 4.65893e6 | 0.957488 | ||||||||
\(474\) | 2.38867e6 | 0.488327 | ||||||||
\(475\) | 770000. | 0.156587 | ||||||||
\(476\) | −433152. | −0.0876240 | ||||||||
\(477\) | −140454. | −0.0282643 | ||||||||
\(478\) | −3.34488e6 | −0.669593 | ||||||||
\(479\) | 2.13461e6 | 0.425088 | 0.212544 | − | 0.977151i | \(-0.431825\pi\) | ||||
0.212544 | + | 0.977151i | \(0.431825\pi\) | |||||||
\(480\) | 230400. | 0.0456435 | ||||||||
\(481\) | 1.47528e6 | 0.290745 | ||||||||
\(482\) | 2.56196e6 | 0.502290 | ||||||||
\(483\) | 152352. | 0.0297153 | ||||||||
\(484\) | −362672. | −0.0703721 | ||||||||
\(485\) | −3.12935e6 | −0.604087 | ||||||||
\(486\) | −236196. | −0.0453609 | ||||||||
\(487\) | 2.48361e6 | 0.474527 | 0.237264 | − | 0.971445i | \(-0.423749\pi\) | ||||
0.237264 | + | 0.971445i | \(0.423749\pi\) | |||||||
\(488\) | −2.21939e6 | −0.421876 | ||||||||
\(489\) | 3.21908e6 | 0.608780 | ||||||||
\(490\) | 1.57830e6 | 0.296961 | ||||||||
\(491\) | 2.81221e6 | 0.526434 | 0.263217 | − | 0.964737i | \(-0.415216\pi\) | ||||
0.263217 | + | 0.964737i | \(0.415216\pi\) | |||||||
\(492\) | 2.27146e6 | 0.423050 | ||||||||
\(493\) | 1.10149e6 | 0.204110 | ||||||||
\(494\) | −1.88250e6 | −0.347070 | ||||||||
\(495\) | −753300. | −0.138183 | ||||||||
\(496\) | 1.49504e6 | 0.272865 | ||||||||
\(497\) | 723072. | 0.131308 | ||||||||
\(498\) | −1.21478e6 | −0.219496 | ||||||||
\(499\) | 7.59100e6 | 1.36473 | 0.682367 | − | 0.731010i | \(-0.260951\pi\) | ||||
0.682367 | + | 0.731010i | \(0.260951\pi\) | |||||||
\(500\) | −250000. | −0.0447214 | ||||||||
\(501\) | −4.80427e6 | −0.855132 | ||||||||
\(502\) | 5.80162e6 | 1.02752 | ||||||||
\(503\) | −4.79856e6 | −0.845651 | −0.422825 | − | 0.906211i | \(-0.638962\pi\) | ||||
−0.422825 | + | 0.906211i | \(0.638962\pi\) | |||||||
\(504\) | 165888. | 0.0290897 | ||||||||
\(505\) | −2.15985e6 | −0.376873 | ||||||||
\(506\) | −787152. | −0.136673 | ||||||||
\(507\) | 2.02832e6 | 0.350443 | ||||||||
\(508\) | 1.74790e6 | 0.300510 | ||||||||
\(509\) | −2.45689e6 | −0.420330 | −0.210165 | − | 0.977666i | \(-0.567400\pi\) | ||||
−0.210165 | + | 0.977666i | \(0.567400\pi\) | |||||||
\(510\) | −761400. | −0.129625 | ||||||||
\(511\) | 1.84326e6 | 0.312274 | ||||||||
\(512\) | 262144. | 0.0441942 | ||||||||
\(513\) | −898128. | −0.150676 | ||||||||
\(514\) | 2.88487e6 | 0.481636 | ||||||||
\(515\) | −3.57380e6 | −0.593762 | ||||||||
\(516\) | −1.80346e6 | −0.298182 | ||||||||
\(517\) | 8.14234e6 | 1.33975 | ||||||||
\(518\) | −494336. | −0.0809465 | ||||||||
\(519\) | −4.71231e6 | −0.767919 | ||||||||
\(520\) | 611200. | 0.0991231 | ||||||||
\(521\) | −1.23443e7 | −1.99239 | −0.996194 | − | 0.0871674i | \(-0.972219\pi\) | ||||
−0.996194 | + | 0.0871674i | \(0.972219\pi\) | |||||||
\(522\) | −421848. | −0.0677610 | ||||||||
\(523\) | −3.78572e6 | −0.605193 | −0.302596 | − | 0.953119i | \(-0.597853\pi\) | ||||
−0.302596 | + | 0.953119i | \(0.597853\pi\) | |||||||
\(524\) | −849600. | −0.135172 | ||||||||
\(525\) | −180000. | −0.0285019 | ||||||||
\(526\) | 3.04915e6 | 0.480524 | ||||||||
\(527\) | −4.94064e6 | −0.774920 | ||||||||
\(528\) | −857088. | −0.133795 | ||||||||
\(529\) | 279841. | 0.0434783 | ||||||||
\(530\) | 173400. | 0.0268139 | ||||||||
\(531\) | 154548. | 0.0237863 | ||||||||
\(532\) | 630784. | 0.0966277 | ||||||||
\(533\) | 6.02567e6 | 0.918728 | ||||||||
\(534\) | −1.31954e6 | −0.200249 | ||||||||
\(535\) | −3.84480e6 | −0.580750 | ||||||||
\(536\) | 1.46509e6 | 0.220268 | ||||||||
\(537\) | 4.02462e6 | 0.602267 | ||||||||
\(538\) | −6.44748e6 | −0.960361 | ||||||||
\(539\) | −5.87128e6 | −0.870484 | ||||||||
\(540\) | 291600. | 0.0430331 | ||||||||
\(541\) | −4.32426e6 | −0.635212 | −0.317606 | − | 0.948223i | \(-0.602879\pi\) | ||||
−0.317606 | + | 0.948223i | \(0.602879\pi\) | |||||||
\(542\) | −3.26819e6 | −0.477870 | ||||||||
\(543\) | −1.44679e6 | −0.210574 | ||||||||
\(544\) | −866304. | −0.125508 | ||||||||
\(545\) | −682250. | −0.0983903 | ||||||||
\(546\) | 440064. | 0.0631734 | ||||||||
\(547\) | −1.10591e7 | −1.58035 | −0.790174 | − | 0.612883i | \(-0.790010\pi\) | ||||
−0.790174 | + | 0.612883i | \(0.790010\pi\) | |||||||
\(548\) | −4.52707e6 | −0.643971 | ||||||||
\(549\) | −2.80892e6 | −0.397748 | ||||||||
\(550\) | 930000. | 0.131092 | ||||||||
\(551\) | −1.60406e6 | −0.225083 | ||||||||
\(552\) | 304704. | 0.0425628 | ||||||||
\(553\) | −2.12326e6 | −0.295251 | ||||||||
\(554\) | 6.35175e6 | 0.879264 | ||||||||
\(555\) | −868950. | −0.119746 | ||||||||
\(556\) | 5.88205e6 | 0.806941 | ||||||||
\(557\) | −1.10752e7 | −1.51257 | −0.756284 | − | 0.654243i | \(-0.772987\pi\) | ||||
−0.756284 | + | 0.654243i | \(0.772987\pi\) | |||||||
\(558\) | 1.89216e6 | 0.257260 | ||||||||
\(559\) | −4.78417e6 | −0.647555 | ||||||||
\(560\) | −204800. | −0.0275969 | ||||||||
\(561\) | 2.83241e6 | 0.379969 | ||||||||
\(562\) | −4.13460e6 | −0.552195 | ||||||||
\(563\) | −3.37164e6 | −0.448302 | −0.224151 | − | 0.974554i | \(-0.571961\pi\) | ||||
−0.224151 | + | 0.974554i | \(0.571961\pi\) | |||||||
\(564\) | −3.15187e6 | −0.417225 | ||||||||
\(565\) | −3.50085e6 | −0.461373 | ||||||||
\(566\) | −2.24248e6 | −0.294230 | ||||||||
\(567\) | 209952. | 0.0274260 | ||||||||
\(568\) | 1.44614e6 | 0.188079 | ||||||||
\(569\) | −781410. | −0.101181 | −0.0505904 | − | 0.998719i | \(-0.516110\pi\) | ||||
−0.0505904 | + | 0.998719i | \(0.516110\pi\) | |||||||
\(570\) | 1.10880e6 | 0.142944 | ||||||||
\(571\) | 2.58882e6 | 0.332285 | 0.166143 | − | 0.986102i | \(-0.446869\pi\) | ||||
0.166143 | + | 0.986102i | \(0.446869\pi\) | |||||||
\(572\) | −2.27366e6 | −0.290560 | ||||||||
\(573\) | −5.93460e6 | −0.755101 | ||||||||
\(574\) | −2.01907e6 | −0.255783 | ||||||||
\(575\) | −330625. | −0.0417029 | ||||||||
\(576\) | 331776. | 0.0416667 | ||||||||
\(577\) | −2.28108e6 | −0.285234 | −0.142617 | − | 0.989778i | \(-0.545552\pi\) | ||||
−0.142617 | + | 0.989778i | \(0.545552\pi\) | |||||||
\(578\) | −2.81656e6 | −0.350671 | ||||||||
\(579\) | 5.90845e6 | 0.732448 | ||||||||
\(580\) | 520800. | 0.0642837 | ||||||||
\(581\) | 1.07981e6 | 0.132711 | ||||||||
\(582\) | −4.50626e6 | −0.551454 | ||||||||
\(583\) | −645048. | −0.0785997 | ||||||||
\(584\) | 3.68653e6 | 0.447286 | ||||||||
\(585\) | 773550. | 0.0934542 | ||||||||
\(586\) | −9.65148e6 | −1.16105 | ||||||||
\(587\) | 577956. | 0.0692308 | 0.0346154 | − | 0.999401i | \(-0.488979\pi\) | ||||
0.0346154 | + | 0.999401i | \(0.488979\pi\) | |||||||
\(588\) | 2.27275e6 | 0.271087 | ||||||||
\(589\) | 7.19488e6 | 0.854546 | ||||||||
\(590\) | −190800. | −0.0225657 | ||||||||
\(591\) | 7.67464e6 | 0.903836 | ||||||||
\(592\) | −988672. | −0.115944 | ||||||||
\(593\) | −9.41105e6 | −1.09901 | −0.549505 | − | 0.835491i | \(-0.685184\pi\) | ||||
−0.549505 | + | 0.835491i | \(0.685184\pi\) | |||||||
\(594\) | −1.08475e6 | −0.126143 | ||||||||
\(595\) | 676800. | 0.0783733 | ||||||||
\(596\) | 176544. | 0.0203581 | ||||||||
\(597\) | −3.71246e6 | −0.426311 | ||||||||
\(598\) | 808312. | 0.0924328 | ||||||||
\(599\) | −9.98084e6 | −1.13658 | −0.568290 | − | 0.822828i | \(-0.692395\pi\) | ||||
−0.568290 | + | 0.822828i | \(0.692395\pi\) | |||||||
\(600\) | −360000. | −0.0408248 | ||||||||
\(601\) | −2.09349e6 | −0.236421 | −0.118210 | − | 0.992989i | \(-0.537716\pi\) | ||||
−0.118210 | + | 0.992989i | \(0.537716\pi\) | |||||||
\(602\) | 1.60307e6 | 0.180286 | ||||||||
\(603\) | 1.85425e6 | 0.207671 | ||||||||
\(604\) | 7.24429e6 | 0.807985 | ||||||||
\(605\) | 566675. | 0.0629427 | ||||||||
\(606\) | −3.11018e6 | −0.344037 | ||||||||
\(607\) | 7.16035e6 | 0.788792 | 0.394396 | − | 0.918941i | \(-0.370954\pi\) | ||||
0.394396 | + | 0.918941i | \(0.370954\pi\) | |||||||
\(608\) | 1.26157e6 | 0.138405 | ||||||||
\(609\) | 374976. | 0.0409695 | ||||||||
\(610\) | 3.46780e6 | 0.377337 | ||||||||
\(611\) | −8.36122e6 | −0.906080 | ||||||||
\(612\) | −1.09642e6 | −0.118331 | ||||||||
\(613\) | 1.32798e7 | 1.42739 | 0.713694 | − | 0.700458i | \(-0.247021\pi\) | ||||
0.713694 | + | 0.700458i | \(0.247021\pi\) | |||||||
\(614\) | 9.02917e6 | 0.966556 | ||||||||
\(615\) | −3.54915e6 | −0.378387 | ||||||||
\(616\) | 761856. | 0.0808949 | ||||||||
\(617\) | 1.15423e6 | 0.122061 | 0.0610306 | − | 0.998136i | \(-0.480561\pi\) | ||||
0.0610306 | + | 0.998136i | \(0.480561\pi\) | |||||||
\(618\) | −5.14627e6 | −0.542028 | ||||||||
\(619\) | −1.62292e7 | −1.70243 | −0.851217 | − | 0.524813i | \(-0.824135\pi\) | ||||
−0.851217 | + | 0.524813i | \(0.824135\pi\) | |||||||
\(620\) | −2.33600e6 | −0.244058 | ||||||||
\(621\) | 385641. | 0.0401286 | ||||||||
\(622\) | −8.11790e6 | −0.841333 | ||||||||
\(623\) | 1.17293e6 | 0.121074 | ||||||||
\(624\) | 880128. | 0.0904866 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 9.94498e6 | 1.01430 | ||||||||
\(627\) | −4.12474e6 | −0.419013 | ||||||||
\(628\) | 5.94358e6 | 0.601380 | ||||||||
\(629\) | 3.26725e6 | 0.329273 | ||||||||
\(630\) | −259200. | −0.0260186 | ||||||||
\(631\) | −3.74248e6 | −0.374185 | −0.187092 | − | 0.982342i | \(-0.559906\pi\) | ||||
−0.187092 | + | 0.982342i | \(0.559906\pi\) | |||||||
\(632\) | −4.24653e6 | −0.422904 | ||||||||
\(633\) | −9.12359e6 | −0.905016 | ||||||||
\(634\) | 8.40262e6 | 0.830217 | ||||||||
\(635\) | −2.73110e6 | −0.268784 | ||||||||
\(636\) | 249696. | 0.0244776 | ||||||||
\(637\) | 6.02911e6 | 0.588714 | ||||||||
\(638\) | −1.93738e6 | −0.188435 | ||||||||
\(639\) | 1.83028e6 | 0.177323 | ||||||||
\(640\) | −409600. | −0.0395285 | ||||||||
\(641\) | −4.58167e6 | −0.440431 | −0.220216 | − | 0.975451i | \(-0.570676\pi\) | ||||
−0.220216 | + | 0.975451i | \(0.570676\pi\) | |||||||
\(642\) | −5.53651e6 | −0.530150 | ||||||||
\(643\) | 5.02392e6 | 0.479198 | 0.239599 | − | 0.970872i | \(-0.422984\pi\) | ||||
0.239599 | + | 0.970872i | \(0.422984\pi\) | |||||||
\(644\) | −270848. | −0.0257342 | ||||||||
\(645\) | 2.81790e6 | 0.266702 | ||||||||
\(646\) | −4.16909e6 | −0.393061 | ||||||||
\(647\) | 2.10269e6 | 0.197476 | 0.0987380 | − | 0.995113i | \(-0.468519\pi\) | ||||
0.0987380 | + | 0.995113i | \(0.468519\pi\) | |||||||
\(648\) | 419904. | 0.0392837 | ||||||||
\(649\) | 709776. | 0.0661469 | ||||||||
\(650\) | −955000. | −0.0886584 | ||||||||
\(651\) | −1.68192e6 | −0.155544 | ||||||||
\(652\) | −5.72282e6 | −0.527219 | ||||||||
\(653\) | −2.09388e7 | −1.92163 | −0.960815 | − | 0.277191i | \(-0.910597\pi\) | ||||
−0.960815 | + | 0.277191i | \(0.910597\pi\) | |||||||
\(654\) | −982440. | −0.0898176 | ||||||||
\(655\) | 1.32750e6 | 0.120901 | ||||||||
\(656\) | −4.03814e6 | −0.366372 | ||||||||
\(657\) | 4.66576e6 | 0.421705 | ||||||||
\(658\) | 2.80166e6 | 0.252262 | ||||||||
\(659\) | −6.17771e6 | −0.554133 | −0.277066 | − | 0.960851i | \(-0.589362\pi\) | ||||
−0.277066 | + | 0.960851i | \(0.589362\pi\) | |||||||
\(660\) | 1.33920e6 | 0.119670 | ||||||||
\(661\) | 1.05622e7 | 0.940267 | 0.470133 | − | 0.882595i | \(-0.344206\pi\) | ||||
0.470133 | + | 0.882595i | \(0.344206\pi\) | |||||||
\(662\) | −9.42030e6 | −0.835449 | ||||||||
\(663\) | −2.90855e6 | −0.256976 | ||||||||
\(664\) | 2.15962e6 | 0.190089 | ||||||||
\(665\) | −985600. | −0.0864264 | ||||||||
\(666\) | −1.25129e6 | −0.109313 | ||||||||
\(667\) | 688758. | 0.0599449 | ||||||||
\(668\) | 8.54093e6 | 0.740566 | ||||||||
\(669\) | 1.63948e6 | 0.141625 | ||||||||
\(670\) | −2.28920e6 | −0.197014 | ||||||||
\(671\) | −1.29002e7 | −1.10609 | ||||||||
\(672\) | −294912. | −0.0251924 | ||||||||
\(673\) | 3.19500e6 | 0.271915 | 0.135958 | − | 0.990715i | \(-0.456589\pi\) | ||||
0.135958 | + | 0.990715i | \(0.456589\pi\) | |||||||
\(674\) | −9.28766e6 | −0.787511 | ||||||||
\(675\) | −455625. | −0.0384900 | ||||||||
\(676\) | −3.60590e6 | −0.303492 | ||||||||
\(677\) | −7.38447e6 | −0.619224 | −0.309612 | − | 0.950863i | \(-0.600199\pi\) | ||||
−0.309612 | + | 0.950863i | \(0.600199\pi\) | |||||||
\(678\) | −5.04122e6 | −0.421174 | ||||||||
\(679\) | 4.00557e6 | 0.333418 | ||||||||
\(680\) | 1.35360e6 | 0.112258 | ||||||||
\(681\) | 637632. | 0.0526869 | ||||||||
\(682\) | 8.68992e6 | 0.715410 | ||||||||
\(683\) | −2.00003e7 | −1.64053 | −0.820265 | − | 0.571984i | \(-0.806174\pi\) | ||||
−0.820265 | + | 0.571984i | \(0.806174\pi\) | |||||||
\(684\) | 1.59667e6 | 0.130489 | ||||||||
\(685\) | 7.07355e6 | 0.575985 | ||||||||
\(686\) | −4.17152e6 | −0.338442 | ||||||||
\(687\) | 1.04629e6 | 0.0845782 | ||||||||
\(688\) | 3.20614e6 | 0.258233 | ||||||||
\(689\) | 662388. | 0.0531575 | ||||||||
\(690\) | −476100. | −0.0380693 | ||||||||
\(691\) | 1.97883e7 | 1.57657 | 0.788286 | − | 0.615308i | \(-0.210969\pi\) | ||||
0.788286 | + | 0.615308i | \(0.210969\pi\) | |||||||
\(692\) | 8.37744e6 | 0.665037 | ||||||||
\(693\) | 964224. | 0.0762684 | ||||||||
\(694\) | 2.60376e6 | 0.205212 | ||||||||
\(695\) | −9.19070e6 | −0.721750 | ||||||||
\(696\) | 749952. | 0.0586827 | ||||||||
\(697\) | 1.33448e7 | 1.04047 | ||||||||
\(698\) | 1.49324e6 | 0.116009 | ||||||||
\(699\) | −1.17823e7 | −0.912090 | ||||||||
\(700\) | 320000. | 0.0246834 | ||||||||
\(701\) | −1.57309e6 | −0.120909 | −0.0604543 | − | 0.998171i | \(-0.519255\pi\) | ||||
−0.0604543 | + | 0.998171i | \(0.519255\pi\) | |||||||
\(702\) | 1.11391e6 | 0.0853116 | ||||||||
\(703\) | −4.75798e6 | −0.363107 | ||||||||
\(704\) | 1.52371e6 | 0.115870 | ||||||||
\(705\) | 4.92480e6 | 0.373178 | ||||||||
\(706\) | −1.16839e7 | −0.882218 | ||||||||
\(707\) | 2.76461e6 | 0.208010 | ||||||||
\(708\) | −274752. | −0.0205995 | ||||||||
\(709\) | −1.21073e7 | −0.904545 | −0.452272 | − | 0.891880i | \(-0.649387\pi\) | ||||
−0.452272 | + | 0.891880i | \(0.649387\pi\) | |||||||
\(710\) | −2.25960e6 | −0.168223 | ||||||||
\(711\) | −5.37451e6 | −0.398717 | ||||||||
\(712\) | 2.34586e6 | 0.173421 | ||||||||
\(713\) | −3.08936e6 | −0.227586 | ||||||||
\(714\) | 974592. | 0.0715447 | ||||||||
\(715\) | 3.55260e6 | 0.259885 | ||||||||
\(716\) | −7.15488e6 | −0.521579 | ||||||||
\(717\) | 7.52598e6 | 0.546720 | ||||||||
\(718\) | −1.43315e7 | −1.03748 | ||||||||
\(719\) | 1.38124e7 | 0.996430 | 0.498215 | − | 0.867054i | \(-0.333989\pi\) | ||||
0.498215 | + | 0.867054i | \(0.333989\pi\) | |||||||
\(720\) | −518400. | −0.0372678 | ||||||||
\(721\) | 4.57446e6 | 0.327719 | ||||||||
\(722\) | −3.83310e6 | −0.273657 | ||||||||
\(723\) | −5.76441e6 | −0.410118 | ||||||||
\(724\) | 2.57206e6 | 0.182362 | ||||||||
\(725\) | −813750. | −0.0574971 | ||||||||
\(726\) | 816012. | 0.0574586 | ||||||||
\(727\) | −455224. | −0.0319440 | −0.0159720 | − | 0.999872i | \(-0.505084\pi\) | ||||
−0.0159720 | + | 0.999872i | \(0.505084\pi\) | |||||||
\(728\) | −782336. | −0.0547098 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | −5.76020e6 | −0.400065 | ||||||||
\(731\) | −1.05953e7 | −0.733365 | ||||||||
\(732\) | 4.99363e6 | 0.344460 | ||||||||
\(733\) | −1.30986e7 | −0.900459 | −0.450230 | − | 0.892913i | \(-0.648658\pi\) | ||||
−0.450230 | + | 0.892913i | \(0.648658\pi\) | |||||||
\(734\) | 1.14365e7 | 0.783526 | ||||||||
\(735\) | −3.55118e6 | −0.242468 | ||||||||
\(736\) | −541696. | −0.0368605 | ||||||||
\(737\) | 8.51582e6 | 0.577508 | ||||||||
\(738\) | −5.11078e6 | −0.345419 | ||||||||
\(739\) | 1.87971e7 | 1.26613 | 0.633066 | − | 0.774098i | \(-0.281796\pi\) | ||||
0.633066 | + | 0.774098i | \(0.281796\pi\) | |||||||
\(740\) | 1.54480e6 | 0.103703 | ||||||||
\(741\) | 4.23562e6 | 0.283381 | ||||||||
\(742\) | −221952. | −0.0147996 | ||||||||
\(743\) | −2.06305e7 | −1.37100 | −0.685500 | − | 0.728072i | \(-0.740416\pi\) | ||||
−0.685500 | + | 0.728072i | \(0.740416\pi\) | |||||||
\(744\) | −3.36384e6 | −0.222794 | ||||||||
\(745\) | −275850. | −0.0182088 | ||||||||
\(746\) | −6.28790e6 | −0.413674 | ||||||||
\(747\) | 2.73326e6 | 0.179217 | ||||||||
\(748\) | −5.03539e6 | −0.329063 | ||||||||
\(749\) | 4.92134e6 | 0.320538 | ||||||||
\(750\) | 562500. | 0.0365148 | ||||||||
\(751\) | −8.25040e6 | −0.533796 | −0.266898 | − | 0.963725i | \(-0.585999\pi\) | ||||
−0.266898 | + | 0.963725i | \(0.585999\pi\) | |||||||
\(752\) | 5.60333e6 | 0.361328 | ||||||||
\(753\) | −1.30536e7 | −0.838965 | ||||||||
\(754\) | 1.98946e6 | 0.127440 | ||||||||
\(755\) | −1.13192e7 | −0.722684 | ||||||||
\(756\) | −373248. | −0.0237516 | ||||||||
\(757\) | 5.05745e6 | 0.320769 | 0.160384 | − | 0.987055i | \(-0.448727\pi\) | ||||
0.160384 | + | 0.987055i | \(0.448727\pi\) | |||||||
\(758\) | 1.96813e6 | 0.124417 | ||||||||
\(759\) | 1.77109e6 | 0.111593 | ||||||||
\(760\) | −1.97120e6 | −0.123793 | ||||||||
\(761\) | 1.26966e7 | 0.794742 | 0.397371 | − | 0.917658i | \(-0.369923\pi\) | ||||
0.397371 | + | 0.917658i | \(0.369923\pi\) | |||||||
\(762\) | −3.93278e6 | −0.245365 | ||||||||
\(763\) | 873280. | 0.0543053 | ||||||||
\(764\) | 1.05504e7 | 0.653936 | ||||||||
\(765\) | 1.71315e6 | 0.105838 | ||||||||
\(766\) | −7.31030e6 | −0.450156 | ||||||||
\(767\) | −728856. | −0.0447356 | ||||||||
\(768\) | −589824. | −0.0360844 | ||||||||
\(769\) | 2.14955e7 | 1.31079 | 0.655393 | − | 0.755288i | \(-0.272503\pi\) | ||||
0.655393 | + | 0.755288i | \(0.272503\pi\) | |||||||
\(770\) | −1.19040e6 | −0.0723546 | ||||||||
\(771\) | −6.49096e6 | −0.393254 | ||||||||
\(772\) | −1.05039e7 | −0.634319 | ||||||||
\(773\) | 2.25149e7 | 1.35525 | 0.677626 | − | 0.735406i | \(-0.263009\pi\) | ||||
0.677626 | + | 0.735406i | \(0.263009\pi\) | |||||||
\(774\) | 4.05778e6 | 0.243465 | ||||||||
\(775\) | 3.65000e6 | 0.218292 | ||||||||
\(776\) | 8.01114e6 | 0.477573 | ||||||||
\(777\) | 1.11226e6 | 0.0660925 | ||||||||
\(778\) | −1.57924e7 | −0.935404 | ||||||||
\(779\) | −1.94336e7 | −1.14738 | ||||||||
\(780\) | −1.37520e6 | −0.0809337 | ||||||||
\(781\) | 8.40571e6 | 0.493114 | ||||||||
\(782\) | 1.79014e6 | 0.104681 | ||||||||
\(783\) | 949158. | 0.0553266 | ||||||||
\(784\) | −4.04045e6 | −0.234768 | ||||||||
\(785\) | −9.28685e6 | −0.537891 | ||||||||
\(786\) | 1.91160e6 | 0.110367 | ||||||||
\(787\) | 3.26608e7 | 1.87971 | 0.939853 | − | 0.341580i | \(-0.110962\pi\) | ||||
0.939853 | + | 0.341580i | \(0.110962\pi\) | |||||||
\(788\) | −1.36438e7 | −0.782745 | ||||||||
\(789\) | −6.86059e6 | −0.392346 | ||||||||
\(790\) | 6.63520e6 | 0.378256 | ||||||||
\(791\) | 4.48109e6 | 0.254649 | ||||||||
\(792\) | 1.92845e6 | 0.109243 | ||||||||
\(793\) | 1.32470e7 | 0.748057 | ||||||||
\(794\) | −2.98252e6 | −0.167893 | ||||||||
\(795\) | −390150. | −0.0218934 | ||||||||
\(796\) | 6.59994e6 | 0.369196 | ||||||||
\(797\) | −1.25271e7 | −0.698561 | −0.349281 | − | 0.937018i | \(-0.613574\pi\) | ||||
−0.349281 | + | 0.937018i | \(0.613574\pi\) | |||||||
\(798\) | −1.41926e6 | −0.0788962 | ||||||||
\(799\) | −1.85172e7 | −1.02615 | ||||||||
\(800\) | 640000. | 0.0353553 | ||||||||
\(801\) | 2.96897e6 | 0.163503 | ||||||||
\(802\) | 2.03495e7 | 1.11717 | ||||||||
\(803\) | 2.14279e7 | 1.17271 | ||||||||
\(804\) | −3.29645e6 | −0.179848 | ||||||||
\(805\) | 423200. | 0.0230174 | ||||||||
\(806\) | −8.92352e6 | −0.483836 | ||||||||
\(807\) | 1.45068e7 | 0.784131 | ||||||||
\(808\) | 5.52922e6 | 0.297944 | ||||||||
\(809\) | 1.86887e7 | 1.00394 | 0.501971 | − | 0.864884i | \(-0.332608\pi\) | ||||
0.501971 | + | 0.864884i | \(0.332608\pi\) | |||||||
\(810\) | −656100. | −0.0351364 | ||||||||
\(811\) | 4.14348e6 | 0.221214 | 0.110607 | − | 0.993864i | \(-0.464721\pi\) | ||||
0.110607 | + | 0.993864i | \(0.464721\pi\) | |||||||
\(812\) | −666624. | −0.0354806 | ||||||||
\(813\) | 7.35343e6 | 0.390179 | ||||||||
\(814\) | −5.74666e6 | −0.303986 | ||||||||
\(815\) | 8.94190e6 | 0.471559 | ||||||||
\(816\) | 1.94918e6 | 0.102477 | ||||||||
\(817\) | 1.54296e7 | 0.808721 | ||||||||
\(818\) | 8.51377e6 | 0.444876 | ||||||||
\(819\) | −990144. | −0.0515809 | ||||||||
\(820\) | 6.30960e6 | 0.327693 | ||||||||
\(821\) | 2.00599e7 | 1.03865 | 0.519327 | − | 0.854576i | \(-0.326183\pi\) | ||||
0.519327 | + | 0.854576i | \(0.326183\pi\) | |||||||
\(822\) | 1.01859e7 | 0.525800 | ||||||||
\(823\) | 1.70837e7 | 0.879188 | 0.439594 | − | 0.898197i | \(-0.355122\pi\) | ||||
0.439594 | + | 0.898197i | \(0.355122\pi\) | |||||||
\(824\) | 9.14893e6 | 0.469410 | ||||||||
\(825\) | −2.09250e6 | −0.107036 | ||||||||
\(826\) | 244224. | 0.0124548 | ||||||||
\(827\) | 9.20222e6 | 0.467874 | 0.233937 | − | 0.972252i | \(-0.424839\pi\) | ||||
0.233937 | + | 0.972252i | \(0.424839\pi\) | |||||||
\(828\) | −685584. | −0.0347524 | ||||||||
\(829\) | 2.73405e7 | 1.38172 | 0.690861 | − | 0.722988i | \(-0.257232\pi\) | ||||
0.690861 | + | 0.722988i | \(0.257232\pi\) | |||||||
\(830\) | −3.37440e6 | −0.170021 | ||||||||
\(831\) | −1.42914e7 | −0.717916 | ||||||||
\(832\) | −1.56467e6 | −0.0783637 | ||||||||
\(833\) | 1.33524e7 | 0.666726 | ||||||||
\(834\) | −1.32346e7 | −0.658864 | ||||||||
\(835\) | −1.33452e7 | −0.662383 | ||||||||
\(836\) | 7.33286e6 | 0.362876 | ||||||||
\(837\) | −4.25736e6 | −0.210052 | ||||||||
\(838\) | 2.17607e7 | 1.07044 | ||||||||
\(839\) | 3.02621e7 | 1.48421 | 0.742104 | − | 0.670285i | \(-0.233828\pi\) | ||||
0.742104 | + | 0.670285i | \(0.233828\pi\) | |||||||
\(840\) | 460800. | 0.0225328 | ||||||||
\(841\) | −1.88159e7 | −0.917352 | ||||||||
\(842\) | −4.92412e6 | −0.239358 | ||||||||
\(843\) | 9.30285e6 | 0.450866 | ||||||||
\(844\) | 1.62197e7 | 0.783767 | ||||||||
\(845\) | 5.63422e6 | 0.271452 | ||||||||
\(846\) | 7.09171e6 | 0.340663 | ||||||||
\(847\) | −725344. | −0.0347405 | ||||||||
\(848\) | −443904. | −0.0211982 | ||||||||
\(849\) | 5.04558e6 | 0.240238 | ||||||||
\(850\) | −2.11500e6 | −0.100407 | ||||||||
\(851\) | 2.04300e6 | 0.0967039 | ||||||||
\(852\) | −3.25382e6 | −0.153566 | ||||||||
\(853\) | 2.36688e7 | 1.11379 | 0.556895 | − | 0.830583i | \(-0.311993\pi\) | ||||
0.556895 | + | 0.830583i | \(0.311993\pi\) | |||||||
\(854\) | −4.43878e6 | −0.208266 | ||||||||
\(855\) | −2.49480e6 | −0.116713 | ||||||||
\(856\) | 9.84269e6 | 0.459123 | ||||||||
\(857\) | −1.25794e6 | −0.0585071 | −0.0292535 | − | 0.999572i | \(-0.509313\pi\) | ||||
−0.0292535 | + | 0.999572i | \(0.509313\pi\) | |||||||
\(858\) | 5.11574e6 | 0.237241 | ||||||||
\(859\) | 3.29526e7 | 1.52373 | 0.761863 | − | 0.647738i | \(-0.224285\pi\) | ||||
0.761863 | + | 0.647738i | \(0.224285\pi\) | |||||||
\(860\) | −5.00960e6 | −0.230971 | ||||||||
\(861\) | 4.54291e6 | 0.208846 | ||||||||
\(862\) | 1.19222e6 | 0.0546499 | ||||||||
\(863\) | −1.04623e7 | −0.478192 | −0.239096 | − | 0.970996i | \(-0.576851\pi\) | ||||
−0.239096 | + | 0.970996i | \(0.576851\pi\) | |||||||
\(864\) | −746496. | −0.0340207 | ||||||||
\(865\) | −1.30898e7 | −0.594828 | ||||||||
\(866\) | 2.27650e6 | 0.103151 | ||||||||
\(867\) | 6.33727e6 | 0.286322 | ||||||||
\(868\) | 2.99008e6 | 0.134705 | ||||||||
\(869\) | −2.46829e7 | −1.10879 | ||||||||
\(870\) | −1.17180e6 | −0.0524874 | ||||||||
\(871\) | −8.74474e6 | −0.390573 | ||||||||
\(872\) | 1.74656e6 | 0.0777844 | ||||||||
\(873\) | 1.01391e7 | 0.450260 | ||||||||
\(874\) | −2.60691e6 | −0.115438 | ||||||||
\(875\) | −500000. | −0.0220775 | ||||||||
\(876\) | −8.29469e6 | −0.365208 | ||||||||
\(877\) | 3.54954e7 | 1.55838 | 0.779190 | − | 0.626788i | \(-0.215631\pi\) | ||||
0.779190 | + | 0.626788i | \(0.215631\pi\) | |||||||
\(878\) | −1.64254e7 | −0.719083 | ||||||||
\(879\) | 2.17158e7 | 0.947991 | ||||||||
\(880\) | −2.38080e6 | −0.103637 | ||||||||
\(881\) | −3.76131e7 | −1.63267 | −0.816337 | − | 0.577575i | \(-0.803999\pi\) | ||||
−0.816337 | + | 0.577575i | \(0.803999\pi\) | |||||||
\(882\) | −5.11369e6 | −0.221342 | ||||||||
\(883\) | 4.47748e7 | 1.93256 | 0.966278 | − | 0.257500i | \(-0.0828989\pi\) | ||||
0.966278 | + | 0.257500i | \(0.0828989\pi\) | |||||||
\(884\) | 5.17075e6 | 0.222548 | ||||||||
\(885\) | 429300. | 0.0184248 | ||||||||
\(886\) | −1.21278e7 | −0.519037 | ||||||||
\(887\) | 621288. | 0.0265145 | 0.0132573 | − | 0.999912i | \(-0.495780\pi\) | ||||
0.0132573 | + | 0.999912i | \(0.495780\pi\) | |||||||
\(888\) | 2.22451e6 | 0.0946678 | ||||||||
\(889\) | 3.49581e6 | 0.148352 | ||||||||
\(890\) | −3.66540e6 | −0.155112 | ||||||||
\(891\) | 2.44069e6 | 0.102996 | ||||||||
\(892\) | −2.91462e6 | −0.122651 | ||||||||
\(893\) | 2.69660e7 | 1.13159 | ||||||||
\(894\) | −397224. | −0.0166223 | ||||||||
\(895\) | 1.11795e7 | 0.466514 | ||||||||
\(896\) | 524288. | 0.0218172 | ||||||||
\(897\) | −1.81870e6 | −0.0754711 | ||||||||
\(898\) | 5.84158e6 | 0.241735 | ||||||||
\(899\) | −7.60368e6 | −0.313780 | ||||||||
\(900\) | 810000. | 0.0333333 | ||||||||
\(901\) | 1.46696e6 | 0.0602015 | ||||||||
\(902\) | −2.34717e7 | −0.960569 | ||||||||
\(903\) | −3.60691e6 | −0.147203 | ||||||||
\(904\) | 8.96218e6 | 0.364748 | ||||||||
\(905\) | −4.01885e6 | −0.163110 | ||||||||
\(906\) | −1.62996e7 | −0.659717 | ||||||||
\(907\) | 7.07352e6 | 0.285507 | 0.142754 | − | 0.989758i | \(-0.454404\pi\) | ||||
0.142754 | + | 0.989758i | \(0.454404\pi\) | |||||||
\(908\) | −1.13357e6 | −0.0456282 | ||||||||
\(909\) | 6.99791e6 | 0.280905 | ||||||||
\(910\) | 1.22240e6 | 0.0489339 | ||||||||
\(911\) | 9.33912e6 | 0.372829 | 0.186415 | − | 0.982471i | \(-0.440313\pi\) | ||||
0.186415 | + | 0.982471i | \(0.440313\pi\) | |||||||
\(912\) | −2.83853e6 | −0.113007 | ||||||||
\(913\) | 1.25528e7 | 0.498382 | ||||||||
\(914\) | 2.98835e7 | 1.18322 | ||||||||
\(915\) | −7.80255e6 | −0.308094 | ||||||||
\(916\) | −1.86006e6 | −0.0732469 | ||||||||
\(917\) | −1.69920e6 | −0.0667300 | ||||||||
\(918\) | 2.46694e6 | 0.0966165 | ||||||||
\(919\) | −2.76880e7 | −1.08144 | −0.540721 | − | 0.841202i | \(-0.681849\pi\) | ||||
−0.540721 | + | 0.841202i | \(0.681849\pi\) | |||||||
\(920\) | 846400. | 0.0329690 | ||||||||
\(921\) | −2.03156e7 | −0.789189 | ||||||||
\(922\) | −5.35990e6 | −0.207649 | ||||||||
\(923\) | −8.63167e6 | −0.333496 | ||||||||
\(924\) | −1.71418e6 | −0.0660504 | ||||||||
\(925\) | −2.41375e6 | −0.0927551 | ||||||||
\(926\) | 1.32563e7 | 0.508038 | ||||||||
\(927\) | 1.15791e7 | 0.442564 | ||||||||
\(928\) | −1.33325e6 | −0.0508207 | ||||||||
\(929\) | 3.75679e7 | 1.42816 | 0.714082 | − | 0.700063i | \(-0.246845\pi\) | ||||
0.714082 | + | 0.700063i | \(0.246845\pi\) | |||||||
\(930\) | 5.25600e6 | 0.199273 | ||||||||
\(931\) | −1.94447e7 | −0.735235 | ||||||||
\(932\) | 2.09463e7 | 0.789893 | ||||||||
\(933\) | 1.82653e7 | 0.686946 | ||||||||
\(934\) | 9.66010e6 | 0.362338 | ||||||||
\(935\) | 7.86780e6 | 0.294323 | ||||||||
\(936\) | −1.98029e6 | −0.0738820 | ||||||||
\(937\) | −1.95495e7 | −0.727422 | −0.363711 | − | 0.931512i | \(-0.618490\pi\) | ||||
−0.363711 | + | 0.931512i | \(0.618490\pi\) | |||||||
\(938\) | 2.93018e6 | 0.108739 | ||||||||
\(939\) | −2.23762e7 | −0.828176 | ||||||||
\(940\) | −8.75520e6 | −0.323181 | ||||||||
\(941\) | −2.17384e7 | −0.800300 | −0.400150 | − | 0.916450i | \(-0.631042\pi\) | ||||
−0.400150 | + | 0.916450i | \(0.631042\pi\) | |||||||
\(942\) | −1.33731e7 | −0.491025 | ||||||||
\(943\) | 8.34445e6 | 0.305575 | ||||||||
\(944\) | 488448. | 0.0178397 | ||||||||
\(945\) | 583200. | 0.0212441 | ||||||||
\(946\) | 1.86357e7 | 0.677046 | ||||||||
\(947\) | 2.97375e7 | 1.07753 | 0.538766 | − | 0.842455i | \(-0.318891\pi\) | ||||
0.538766 | + | 0.842455i | \(0.318891\pi\) | |||||||
\(948\) | 9.55469e6 | 0.345299 | ||||||||
\(949\) | −2.20040e7 | −0.793114 | ||||||||
\(950\) | 3.08000e6 | 0.110724 | ||||||||
\(951\) | −1.89059e7 | −0.677869 | ||||||||
\(952\) | −1.73261e6 | −0.0619595 | ||||||||
\(953\) | −1.85027e7 | −0.659937 | −0.329969 | − | 0.943992i | \(-0.607038\pi\) | ||||
−0.329969 | + | 0.943992i | \(0.607038\pi\) | |||||||
\(954\) | −561816. | −0.0199859 | ||||||||
\(955\) | −1.64850e7 | −0.584899 | ||||||||
\(956\) | −1.33795e7 | −0.473474 | ||||||||
\(957\) | 4.35910e6 | 0.153857 | ||||||||
\(958\) | 8.53843e6 | 0.300583 | ||||||||
\(959\) | −9.05414e6 | −0.317908 | ||||||||
\(960\) | 921600. | 0.0322749 | ||||||||
\(961\) | 5.47645e6 | 0.191289 | ||||||||
\(962\) | 5.90114e6 | 0.205588 | ||||||||
\(963\) | 1.24572e7 | 0.432866 | ||||||||
\(964\) | 1.02478e7 | 0.355173 | ||||||||
\(965\) | 1.64124e7 | 0.567352 | ||||||||
\(966\) | 609408. | 0.0210119 | ||||||||
\(967\) | −3.53024e6 | −0.121405 | −0.0607026 | − | 0.998156i | \(-0.519334\pi\) | ||||
−0.0607026 | + | 0.998156i | \(0.519334\pi\) | |||||||
\(968\) | −1.45069e6 | −0.0497606 | ||||||||
\(969\) | 9.38045e6 | 0.320933 | ||||||||
\(970\) | −1.25174e7 | −0.427154 | ||||||||
\(971\) | 3.69827e6 | 0.125878 | 0.0629391 | − | 0.998017i | \(-0.479953\pi\) | ||||
0.0629391 | + | 0.998017i | \(0.479953\pi\) | |||||||
\(972\) | −944784. | −0.0320750 | ||||||||
\(973\) | 1.17641e7 | 0.398361 | ||||||||
\(974\) | 9.93445e6 | 0.335542 | ||||||||
\(975\) | 2.14875e6 | 0.0723893 | ||||||||
\(976\) | −8.87757e6 | −0.298311 | ||||||||
\(977\) | −2.36072e6 | −0.0791239 | −0.0395620 | − | 0.999217i | \(-0.512596\pi\) | ||||
−0.0395620 | + | 0.999217i | \(0.512596\pi\) | |||||||
\(978\) | 1.28763e7 | 0.430472 | ||||||||
\(979\) | 1.36353e7 | 0.454682 | ||||||||
\(980\) | 6.31320e6 | 0.209983 | ||||||||
\(981\) | 2.21049e6 | 0.0733358 | ||||||||
\(982\) | 1.12488e7 | 0.372245 | ||||||||
\(983\) | −4.47830e7 | −1.47819 | −0.739094 | − | 0.673603i | \(-0.764746\pi\) | ||||
−0.739094 | + | 0.673603i | \(0.764746\pi\) | |||||||
\(984\) | 9.08582e6 | 0.299141 | ||||||||
\(985\) | 2.13184e7 | 0.700108 | ||||||||
\(986\) | 4.40597e6 | 0.144327 | ||||||||
\(987\) | −6.30374e6 | −0.205971 | ||||||||
\(988\) | −7.52998e6 | −0.245415 | ||||||||
\(989\) | −6.62520e6 | −0.215381 | ||||||||
\(990\) | −3.01320e6 | −0.0977102 | ||||||||
\(991\) | −2.31755e7 | −0.749626 | −0.374813 | − | 0.927100i | \(-0.622293\pi\) | ||||
−0.374813 | + | 0.927100i | \(0.622293\pi\) | |||||||
\(992\) | 5.98016e6 | 0.192945 | ||||||||
\(993\) | 2.11957e7 | 0.682141 | ||||||||
\(994\) | 2.89229e6 | 0.0928486 | ||||||||
\(995\) | −1.03124e7 | −0.330219 | ||||||||
\(996\) | −4.85914e6 | −0.155207 | ||||||||
\(997\) | 3.20121e7 | 1.01994 | 0.509972 | − | 0.860191i | \(-0.329656\pi\) | ||||
0.509972 | + | 0.860191i | \(0.329656\pi\) | |||||||
\(998\) | 3.03640e7 | 0.965012 | ||||||||
\(999\) | 2.81540e6 | 0.0892537 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 690.6.a.a.1.1 | ✓ | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.6.a.a.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial |